In practice, people find that implicit MPC controllers can be well approximated by a more efficient NN controller [1]}.
However, it is not easy to certify stability of the closed-loop system without bounding approximation errors between the NN controller and the original MPC controller.
\(\mathbf {x}[i+1] = f(\mathbf {x}[i], u_{\textnormal {NN}}(\mathbf {x}[i])).\) 
